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Rank Theorem in Infinite Dimension and Lagrange Multipliers

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Abstract

We use an extension to the infinite dimension of the rank theorem of the differential calculus to establish a Lagrange theorem for optimization problems in Banach spaces. We provide an application to variational problems on a space of bounded sequences under equality constraints.

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Acknowledgements

I thank the reviewers very much for helping me improve the contents of the paper, especially the one who kept me from making a mathematical mistake and whose suggestions were very useful and constructive.

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  1. Laboratoire SAMM EA 4543, Université Paris 1 Panthéon-Sorbonne, Centre P.M.F., 90 rue de Tolbiac, 75634, Paris Cedex 13, France

    Joël Blot

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  1. Joël Blot
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Correspondence to Joël Blot.

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Blot, J. Rank Theorem in Infinite Dimension and Lagrange Multipliers. Appl Math Optim 81, 815–822 (2020). https://doi.org/10.1007/s00245-018-9520-y

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  • DOI: https://doi.org/10.1007/s00245-018-9520-y

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